Quantifying the Driving Effect of Colored Noise in Brownian Motors

The colored noise disrupts the detailed balance, enabling directed transport in ratchet systems without additional driving forces. Despite a well-established understanding of the conditions for Brownian motors, quantification of the driving effect of colored noise and its connection to deviations from equilibrium remains unexplored. In this study, we examined the directed motion of an overdamped Brownian motor within an asymmetric traveling potential subjected to Ornstein–Uhlenbeck colored noise. We propose a scheme to quantify the driving effect of colored noise by defining an effective force based on the stopping velocity of the traveling potential where directed transport halts. Our results revealed a nonmonotonic dependence of the effective force on the noise correlation time and a monotonic dependence on the noise strength, corresponding to double and single current reversals, respectively. The nonmonotonicity of the current is attributed to the interplay between the fluctuating characteristics and the driving effects of colored noise.